(c) 2001 w.h. freeman and company chapter 15: temporal and spatial dynamics of populations robert e....

(c) 2001 W.H. Freeman and Company

Chapter 15: Temporal and Spatial Dynamics of Populations

Robert E. RicklefsThe Economy of Nature, Fifth Edition


Chapter Opener


Some populations exhibit regular fluctuations.

Charles Elton first called attention to regular population cycles in 1924: such cycles were known to earlier

naturalists, but Elton brought the matter more widely to the attention of biologists

Elton also called attention to parallel fluctuations in populations of predators and their prey


Evidence for Cycles in Natural Populations

Records of the Hudson’s Bay Company yield important data on fluctuations of animals trapped in northern Canada: data for the snowshoe hare雪兔 (prey) and the

lynx猞猁 (predator) have been particularly useful thousand-fold fluctuations are evident in these

records

Records of gyrfalcons毛隼 exported from Iceland in the mid-eighteenth century also provide evidence for dramatic natural population fluctuations.


Figure 15.1


Figure 15.2


Fluctuations in Populations

Populations are driven by density-dependent factors toward equilibrium numbers.

However, populations also fluctuate about such equilibria平衡 because: populations respond to changes in

environmental conditions:direct effects of temperature, moisture, etc.indirect environmental effects (on food supply, for

example)

populations may be inherently unstable


Fluctuations of Fragmented Populations

Dynamics of individual subpopulations vary from one another: ecological conditions vary from place to place subpopulations are isolated to some degree

and behave partly independently

Changes in a subdivided population are the sum of changes in its subpopulations: subdivided populations thus have unique

properties


Fluctuation is the rule for natural populations.

Tasmanian sheep and Lake Erie伊利湖 phytoplankton both exhibit different degrees of variability in population size: the sheep population is inherently stable:

sheep are large and have greater capacity for homeostasis

the sheep population consists of many overlapping generations

phytoplankton populations are inherently unstable:phytoplankton have reduced capacity for homeostatic内稳

态 regulationpopulations turn over rapidly


Figure 15.3


Figure 15.4


Periodic cycles may or may not coincide for many species.

Populations of similar species may not exhibit synchrony同步 in their fluctuations: four moth飞蛾 species feeding on the same

plant materials in a German forest showed little synchrony in population fluctuations

4-5 year population cycles of small mammals in northern Finland were regular and synchronized across species


Figure 15.5


Temporal variation affects the age structure of populations.

Sizes of different age classes provide a history of past population changes: a good year for spawning and recruitment may

result in a cohort同龄群 that dominates progressively older classes for years to come

The age structure in stands of forest trees may reflect differences in recruitment patterns: some species (such as pine) recruit well only after

a disturbance other species (such as beech山毛榉 ) are shade-

tolerant and recruit almost continuously


Figure 15.7


Figure 15.8

毒芹


Population cycles result from time delays.

A paradox: environmental fluctuations occur

randomly:frequencies of intervals between peaks in

tree-ring width are distributed randomly

populations of many species cycle in a non-random fashion:frequencies of intervals between population

peaks in red fox are distributed non-randomly


Figure 15.9


Figure 15.10


A Mechanism for Population Cycles?

Populations acquire “momentum动力” when high birth rates at low densities cause the populations to overshoot their carrying capacities.

Populations then overcompensate with low survival rates and fall well below their carrying capacities.

The main intrinsic causes of population cycling are time delays时滞 in the responses of birth and death rates to environmental change.


Time Delays and Oscillations震荡 : Discrete-Time Models

Discrete-time models of population dynamics have a built-in time delay: response of population to conditions at one

time is not expressed until the next time interval

continuous readjustment再调整 to changing conditions is not possible

population will thus oscillate as it continually over- and undershoots its carrying capacity


Oscillation Patterns - Discrete Models

Populations with discrete growth can exhibit one of three patterns: r0 small:

population approaches K and stabilizes

r0 exceeds 1 but is less than 2:population exhibits damped oscillations

r0 exceeds 2:population may exhibit limit cycles or (for

high r0) chaos混乱


Figure 15.11


Time Delays and Oscillations: Continuous-Time ModelsContinuous-time models have no

built-in time delays: time delays result from the developmental

period that separates reproductive episodes between generations

a population thus responds to its density at some time in the past, rather than the present

the explicit time delay term added to the logistic equation is tau (t)


Oscillation Patterns - Continuous Models

Populations with continuous growth can exhibit one of three patterns, depending on the product of r and τ: rτ < e-1 (about 0.37):

population approaches K and stabilizes

rτ < π/2 (about 1.6):population exhibits damped oscillations

rτ > π/2:population exhibits limits cycles, with period 4τ -

5τ


Cycles in Laboratory Populations

Water fleas, Daphnia, can be induced to cycle: at higher temperature (25oC), Daphnia magna

exhibits oscillations:period of oscillation is 60 days, suggesting a time delay of

12-15 daysthis is explained as follows: when the population

approaches high density, reproduction ceases; the population declines, leaving mostly senescent individuals; a new cycle requires recruitment of young, fecund individuals

at lower temperature (18oC), the population fails to cycle, because of little or no time delay of responses


Figure 15.12


Storage can promote time delays.

The water flea Daphnia galeata盔形溞stores lipid droplets and can transfer

these to offspring: stored energy introduces a delay in response to

reduced food supplies at high densities Daphnia galeata exhibits pronounced limit

cycles with a period of 15-20 days another water flea, Bosmina longirostris, stores

smaller amount of lipids and does not exhibit oscillations under similar conditions


Figure 15.13


Figure 15.14


Overview of Cyclic BehaviorDensity dependent effects may be delayed

by development time and by storage of nutrients.

Density-dependent effects can act with little delay when adults produce eggs quickly from resources stored over short periods.

Once displaced from an equilibrium at K, behavior of any population will depend on the nature of time delay in its response.


Metapopulations are discrete subpopulations.

Some definitions: areas of habitat with necessary resources

and conditions for population persistence are called habitat patches, or simply patches

individuals living in a habitat patch constitute a subpopulation

a set of subpopulations interconnected by occasional movement between them is called a metapopulation


Figure 15.15


Metapopulation models help managers.

As natural populations become increasingly fragmented by human activities, ecologists have turned increasingly to the metapopulation concept.

Two kinds of processes contribute to dynamics of metapopulations: growth and regulation of subpopulations within

patches colonization to form new subpopulations and

extinction of existing subpopulations


Connectivity determines metapopulation dynamics.

When individuals move frequently between subpopulations, local fluctuations are damped out.

At intermediate levels of movement: the metapopulation behaves as a shifting mosaic

of occupied and unoccupied patches

At low levels of movement: the subpopulations behave independently as small subpopulations go extinct, they cannot be

reestablished, and the entire population eventually goes extinct


The Basic Model of Metapopulation Dynamics

The basic model of metapopulation dynamics predicts the equilibrium proportion of occupied patches, ŝ:

ŝ = 1 - e/cwhere e = probability of a subpopulation going extinct

c = rate constant for colonization

The model predicts a stable equilibrium because when p (proportion of patches occupied) is below the equilibrium point, colonization exceeds extinction, and vice versa.


Behavior of the Metapopulation Model

The relative rates of extinction and colonization (e/c) are of critical importance. when e = 0, ŝ = 1 and all patches are occupied when e = c, ŝ = 0, and the metapopulation

heads toward extinction when 0 < e < c, the result is a shifting mosaic

of occupied and unoccupied patches, with the value of s somewhere between 0 and 1


Is the metapopulation model realistic?

Several unrealistic assumptions are made: all patches are equal rates of colonization and extinction for all

patches are the same

In natural settings: patches vary in size, habitat quality, and

degree of isolation larger subpopulations have lower probabilities

of extinction


The Rescue Effect

Immigration from a large, productive subpopulation can keep a declining subpopulation from going extinct: this is known as the rescue effect救援效应 the rescue effect is incorporated into

metapopulation models by making the rate of extinction (e) decline as the fraction of occupied patches increases

the rescue effect can produce positive density dependence, in which survival of subpopulations increases with more numerous subpopulations


Chance events may cause small populations to go extinct.

Deterministic models assume large populations and no variation in the average values of birth and death rates.

Randomness may affect populations in the real world, however: populations may be subjected to catastrophes灾变 other factors may exert施加 continual influences on

rates of population growth and carrying capacity stochastic (random sampling) processes can also

result in variation, even in a constant environment


Understanding Stochasticity

Consider a coin-tossing experiment: on average, a coin tossed 10 times will

turn up 5 heads and 5 tails, but other possibilities exist:a run with all heads occurs 1 in 1,024 trialsif we equate a “tail” as a death in a population

where each individual has a 0.5 chance of dying, there is a 1 in 1,024 chance of the population going extinct

for a population of 5 individuals, the probability of going extinct is 1 in 32


Stochasticity can affect births.

Consider a population in which only births occur, such that N(t) = N(0)ebt.

On average we expect the population to grow by a factor of 1.65 (e0.5) in one time interval.

For a small population of 5 individuals: the average size after one time interval would

be 5 x 1.65 = 8.24, but this could vary from as few as 5 to as many as 20, just by chance


Stochastic Extinction of Small Populations

Theoretical models exist for predicting the probability of extinction of populations because of stochastic events.

For a simple model in which birth and death rates are equal, the probability of extinction increases with: smaller population size larger b (and d) time


Stochastic Extinction with Density Dependence

Most stochastic models do not include density-dependent changes in birth and death rates. Is this reasonable? density-dependence of birth and death

rates would greatly improve the probability that a population would persist

however, density-independent stochastic models may be realistic for several reasons...


Figure 15.19


Density-independent stochastic models are relevant.The more conservative density-independent

stochastic models are relevant to present-day fragmented populations for several reasons: most subpopulations are now severely isolated changing environments are likely to reduce fecundity when populations are low, the individuals still compete

for resources with larger populations of other species small populations may exhibit positive density-

dependence because of inbreeding effects and problems in locating mates


Size and Extinction of Natural Populations

Evidence for the relationship between population size and the likelihood of extinction comes from studies of avifauna 鸟类 on the California Channel Islands: smaller islands lost a greater proportion of

species than larger islands over a 51-year period

proportions of populations disappearing over this interval were also related to population size


Figure 15.20


Summary 1

Populations of most species fluctuate over time, although the degree of fluctuation varies considerably by species. Some species exhibit regular cyclic fluctuations.

Both discrete and continuous population models show how species populations may oscillate震荡 .


Summary 2

Population oscillations predicted by models are caused by time delays in the responses of individuals to density. Such delays are also responsible for oscillations in natural populations.

Metapopulations are divided into discrete subpopulations, whose dynamics depend in part on migration of individuals between patches.

The dynamics of small populations depend to a large degree on stochastic events.

(c) 2001 w.h. freeman and company chapter 15: temporal and spatial dynamics of populations robert e....

Documents

company figure

unstable slide

prey slide

company evidence

company chapter opener

edition slide

company periodic cycles

population fluctuations